Interesting question. I looked up "phase" in the OED, that great authority on the history of English words, but all I found was confusion.
Here's the "zoological" part of the definition
Zool. A particular period of an animal's life, distinguished by a characteristic form, colour of type of behaviour.
But this is contradicted in the list of examples by: ". . .the dark phase of Eleanora's falcon", the color phases of which are permanent affairs (like those of Screech Owl) not seasonal/developmental as implied by the definition.
So, the mystery remains.
Lesser dictionaries (e.g.the unabridged Random House) not surprisingly given the current zoological usages define "color phase" quite straight-forwardly to mean either a permanent or temporary state.